The height of a cone is 30cm. A small cone is cut of at the top by a plane parallel to the base. Its Volume is 1/27 of the Volume of the given cone then at what Height above the base the section has been made.
Answers
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Answer:
20 cm
Step-by-step explanation:
From figure:
In ΔAPE and ΔAQC,
⇒ ∠PAE = ∠QAC
∴ΔAPE ~ ΔAQC
⇒ PE/QC = AP/AQ
⇒ r/R = h/H
⇒ r/R = h/30
⇒ r = Rh/30
Given that volume is (1/27) of the volume of the given cone.
⇒ (1/3)πr²h = (1/27) * (1/3)πR²H
⇒ (1/3) * (Rh/30)² * h = (1/27) * R² * 30
⇒ (R² * h² * h)/900 = (30/27) * R²
⇒ h³ = (30 * 900)/27
⇒ h³ = 1000
⇒ h = 10 cm
∴ Height above the base = AQ - AP
= H - h
= 30 - 10
= 20 cm.
Therefore, the height = 20 cm.
Note: For the better understanding, i have taken this picture as reference.
Hope it helps!
